1. Field of the Invention
The present invention relates to computerized cryptographic methods for communications in a computer network or electronic communications system, and particularly to an elliptic polynomial-based message authentication code.
2. Description of the Related Art
In recent years, the Internet community has experienced explosive and exponential growth. Given the vast and increasing magnitude of this community, both in terms of the number of individual users and web sites, and the sharply reduced costs associated with electronically communicating information, such as e-mail messages and electronic files, between one user and another, as well as between any individual client computer and a web server, electronic communication, rather than more traditional postal mail, is rapidly becoming a medium of choice for communicating information. The Internet, however, is a publicly accessible network, and is thus not secure. The Internet has been, and increasingly continues to be, a target of a wide variety of attacks from various individuals and organizations intent on eavesdropping, intercepting and/or otherwise compromising or even corrupting message traffic flowing on the Internet, or further illicitly penetrating sites connected to the Internet.
Encryption by itself provides no guarantee that an enciphered message cannot or has not been compromised during transmission or storage by a third party. Encryption does not assure integrity due to the fact that an encrypted message could be intercepted and changed, even though it may be, in any instance, practically impossible, to cryptanalyze. In this regard, the third party could intercept, or otherwise improperly access, a ciphertext message, then substitute a predefined illicit ciphertext block(s), which that party, or someone else acting in concert with that party, has specifically devised for a corresponding block(s) in the message. The intruding party could thereafter transmit the resulting message with the substituted ciphertext block(s) to the destination, all without the knowledge of the eventual recipient of the message.
The field of detecting altered communication: is not confined to Internet messages. With the burgeoning use of stand-alone personal computers, individuals or businesses often store confidential information within the computer, with a desire to safeguard that information from illicit access and alteration by third parties. Password controlled access, which is commonly used to restrict access to a given computer and/or a specific file stored thereon, provides a certain, but rather rudimentary, form of file protection. Once password protection is circumvented, a third party can access a stored file and then change it, with the owner of the file then being completely oblivious to any such change.
In order to ensure message integrity, systems that depend on a shared secret key often rely upon message authentication codes (MACs). The MAC is uses the secret key and the message text to produce a bit string unique to the key and the text of the message, the bit string being appended to the message. The MAC bit string is usually compressed to a fixed number of bits, so that it is much shorter than the message text. When a recipient is able to use his secret key and the text message to generate a MAC that is identical to the MAC appended to the message, the recipient can be confident in the integrity of the message, i.e., that the message has not been altered.
A number of encryption techniques have been used to generate MACs. Some MACs are generated using block ciphers, such as the MAC made with DES. Such MACs, however, are vulnerable to brute force attacks. Other MACs are generated using hash functions, such as MD5, RIPEMD-160, SHA-1, etc. One popular MAC is HMAC, which combines a secret key with a non-keyed hash function, such as SHA-1 or MD5. However, such MACs rely upon the invulnerability of the hash function for their security against various forms of attack. However, the security of such hash functions against attacks has come into question because of successful attacks and evidence of their vulnerability to collisions. None of the current MAC generation algorithms incorporate a hash function that is based upon a mathematically hard problem, and particularly not the elliptic polynomial discrete logarithm problem.
Thus, an elliptic polynomial-based message authentication code solving the aforementioned problems is desired.